1. **State the problem:** Simplify the expression $-4(2x-5y)$. 2. **Formula and rule:** Use the distributive property: $a(b+c) = ab + ac$. 3. **Apply distributive property:** $$-4(2x-5y) = -4 \times 2x + (-4) \times (-5y)$$ 4. **Multiply each term:** $$= -8x + 20y$$ 5. **Final answer:** The simplified expression is $-8x + 20y$.